2 1 Introduction Can stock market returns be predicted? This question is central to asset pricing, portfolio choice, and risk management. The general finding in the literature is that price-based financial variables tend to predict stock returns better than quantity-based macroeconomic indicators (Campbell, 2003; Cochrane, 2008; Lettau and Ludvigson, 2009; among others). This finding is discomfiting, as expected returns should ultimately be linked to the business cycle. In fact, a countercyclical risk premium is predicted by almost all leading asset pricing models, whether they are consumption-based (Campbell and Cochrane, 1999; Bansal and Yaron, 2004; among others) or production-based (Cochrane, 1991; Zhang, 2005; Li, Livdan, and Zhang, 2009; Liu, Whited, and Zhang, 2009; among others). However, many of the traditional business cycle variables, such as the growth rate of the GDP, do not forecast stock returns (Pena, Restoy, and Rodriguez, 2002). One recent exception (Cooper and Priestley, 2009) finds that the deviation of log industrial production from its long-run trend, also known as the output gap, predicts stock market returns well. In this paper, we propose a novel yet simple business cycle variable that predicts stock market returns well, and even outperforms the output gap when used in real time. This variable is the growth rate of the aggregate industrial usage of electricity. Most modern industrial production activities involve the use of electricity. Crucially, due to technological limitations, electricity cannot easily be stored. As a result, industrial electricity usage can be used to track production and output in real time. 1 Indeed, since 1971, the Federal Reserve has been using survey data on electric power when estimating key components of their monthly industrial production index. The practice was 1 As anecdotal evidence, the Chinese premier relies on electricity consumption as a more accurate measure of economic growth in China. All other figures, especially GDP statistics, are man-made and therefore unreliable. See the Wall Street Journal, December 6,

3 discontinued in 2005, due to poor survey coverage. 2 Since electric utilities are highly regulated and are subject to extensive disclosure requirements, electricity usage data are accurately measured and reported. For these reasons, the business cycle literature has long used industrial electricity usage as a proxy for capital services (Jorgenson and Griliches, 1967; Burnside, Eichenbaum, and Rebelo, 1995 and 1996; Comin and Gertler, 2006). Capacity utilization, which is reflected in industrial electricity usage, appears to be the key missing ingredient that allows a relatively mild productivity shock to drive a much more volatile business cycle (King and Rebelo, 2000). Despite the importance of industrial electricity usage as a business cycle variable, its predictive power on stock market returns has not been examined in the literature. Our paper fills this gap. Since monthly industrial electricity usage data are available in the United States in our sample period, , we first conduct overlapping monthly predictive regressions to maximize the power of the test. To alleviate the impact of within-year seasonality in electricity usage, we compute year-over-year growth rates. For example, we use the industrial electricity growth rate from January in year t 1 to January in year t to predict the excess stock return in February in year t. We then use the electricity growth rate from February in year t 1 to February in year t to predict the excess stock return in March in year t, and so on. Stambaugh (1999) argues that predictive regressions potentially lead to overestimated t-values with a small sample in an overlapping regression because many predictive variables are persistent. To address this bias, we follow Li, Ng, and Swaminathan (2013) closely, and report p-values from simulation exercises. For comparison purposes, we also report the more standard Hodrick (1992) t-value. We find that this simple year-over-year industrial electricity usage growth rate has 2 The survey was conducted by the regional Federal Reserve Banks of the electric utilities in their district; it was not the Department of Energy/Energy Information Administration survey that we use in this paper. 3

4 strong and significant predictive power for future stock market excess returns in horizons ranging from one month up to one year. At the annual horizon, a 1% increase in the year-over-year industrial electricity usage growth rate predicts an excess stock return that is 0.92% lower in the next year, with an R-squared of 8.64%. Compared to commercial and residential electricity usage, industrial electricity usage is less affected by weather conditions. Nevertheless, to make sure our results are not driven by weather changes, we orthogonalize industrial electricity growth on a weather change variable and focus on the residual. The weather-adjusted electricity usage growth rate produces very similar results, suggesting that any potential weather effect remnants in our year-over-year electricity growth rate are not driving the predictive results. The in-sample predictive power of the industrial electricity usage growth rate compares favorably to 10 well-known return predictors that are based on financial information. These predictive variables include dividend-price ratio, earnings-price ratio, bookto-market ratio, Treasury bill rates, the default premium, the term premium, net equity issuance, inflation, returns on long-term government bonds, and stock variance. These predictors are associated with much lower R-squares and their regression coefficients are in general insignificant, with the inflation rate and the returns on long-term government bonds as the exceptions. When we include industrial electricity usage growth with the ten predictors, one at a time, in the same predictive regression, electricity growth drives out all the financial variables except the inflation rate and the returns on long-term government bonds. We also compare industrial electricity growth to several predictors that are based directly on industrial production. The first is the year-over-year growth rate in monthly industrial production. The second is the year-over-year change in monthly capital utilization. The next two are production growth from the fourth quarter of the previous year to the fourth quarter of this year and production growth from the third quarter of 4

5 this year to the fourth quarter of this year. The last predictor is the in-sample output gap investigated by Cooper and Priestley (2009), who measure the gap as the deviation of log industrial production from its long-run trend using the full sample for regression. These five measures are all highly correlated with industrial electricity growth. At annual frequency, the correlations of industrial electricity growth with industrial output growth from December to December, or fourth quarter to fourth quarter, or third quarter to fourth quarter, and capacity utilization, are all above 60%; the correlation with the insample output gap is lower, but still at 36%. The high correlations are not surprising, as industrial-output-based measures, just like industrial electricity usage, are business cycle variables, as evident in their high correlations with the NBER expansion indicator. Which business cycle variable is the best predictor of future market returns? We find the in-sample output gap to be the strongest predictor. It has an R-squared of more than 16% for predicting next-year market excess returns and the regression slope coefficients are highly significant. Nevertheless, we find that industrial electricity usage growth comes in second, and it outperforms the remaining industrial-output-based measures, including various versions of industrial output growth, capacity utilization, and the out-of-sample output gap, which computes the gap using backward rolling windows. In addition, even though the in-sample output gap outperforms industrial electricity usage growth on a stand alone basis, when they are included in the same regression, we find that industrial electricity usage growth remains significant. This finding suggests that industrial electricity usage has incremental return predictive power. How can industrial electricity growth outperform the industrial output growth rate in predicting future stock returns? We examine this question in detail by zooming in on industrial output from the 14 different industries that account for most of the total industrial output. We first regress the output growth in each industry on the electricity growth rate. The regression coefficient therefore measures the output s sensitivity to elec- 5

6 tricity usage for each industry. The industries with the highest sensitivity to electricity usage are steel, machinery, fabricated products, and construction. These industries are likely to be more capital-intensive, which is consistent with the high sensitivity of their output to electricity usage. 3 The output growth rates of these four industries are highly cyclical. One reason is that they produce capital goods used by other firms to make their own products. When demand is slack, few firms will expand and purchase capital goods. As such, capital goods producers bear the brunt of a slowdown but perform well in good times. Another reason is that these capital-intensive producers often have higher operating leverage and therefore are more exposed to business cycle fluctuations. Indeed, we find the output growth of these four industries with high sensitivities to electricity usage to have strong predictive power for future stock returns. In sharp contrast, the output growth of the remaining industries, which have modest or low sensitivity to electricity usage, has little return predictive power. This finding suggests that industrial electricity usage appears to be a good measure of output in the very cyclical industries, which explains why it performs better than the total industrial output in forecasting stock returns. The predictability of stock returns is typically taken out of sample. Welch and Goyal (2008) show that none of the existing predicting variables outperforms the historical mean in their out-of-sample experiment. For this reason, we evaluate the performance of the industrial electricity growth rate and other return predictors using the out-of-sample test methodology of Campbell and Thompson (2008). While most financial variables underperform the historical mean in the out-of-sample test, industrial electricity growth rate beats it, and by the largest margin. When compared to the other industrial-outputbased measures, the only variable that outperforms industrial electricity growth is the in-sample output gap. 3 See discussion in Industrial Production and Capacity Utilization: The 2005 Annual Revision, page A50. 6

7 Since industrial electricity usage data is available only at annual frequency in the United Kingdom and Japan, we also conduct annual predictive regressions, where the dependent variable is always excess stock returns in the next calendar year. These annual regressions allow us to examine the performance of industrial electricity growth beyond the United States, and also to compare it to other output measures. Moreover, annual regressions avoid the use of overlapping samples and are less subject to statistical inference bias. Several interesting patterns emerge from these annual-horizon analyses in all three countries. First, the annual industrial electricity usage growth rate by itself remains a good predictor of future excess stock returns; its regression R-squares are 10.15% in the U.S., 6.95% in Japan, and 11% in the UK. Second, industrial electricity usage growth clearly outperforms the year-over-year output growth, because when these two are combined, electricity has much higher t-values and lower p-values for all three countries. Third, when industrial electricity usage is combined with various output growth measures as analyzed in Moller and Rangvid (2014), we find that industrial electricity usually outperforms other variables. The only exception is that it underperforms the output growth of the third quarter of this year to the fourth quarter of this year in the United States. Finally, while Cooper and Priestley s (2009) output gap measure forecasts stock market returns better on a standalone basis, it does not drive out the electricity growth rate in the United States. In fact, industrial electricity usage growth rates often have higher t- values than the output gap does in head-to-head comparisons. In other words, industrial electricity usage contains valuable and incremental information that helps predict future stock returns. We could also compare industrial electricity usage growth to investment growth rates using annual predictive regressions in the US, where quarterly investment data is available. Not surprisingly, investment growth rates, output growth rates, and the industrial 7

8 electricity growth rate are all highly correlated at annual frequency. We find annual investment growth rates, computed from fourth quarter to fourth quarter and from third quarter to fourth quarter, have predictive power on next-year excess stock returns. These findings provide further empirical support for the investment-based asset pricing literature. As argued by Cochrane (1991), and more recently by Lin and Zhang (2013), under fairly general assumptions, investment today should negatively predict stock returns tomorrow. Nevertheless, industrial electricity usage growth still does a much better job than investment growth in predicting future excess stock returns in univariate regressions, and drives out investment growth in multivariate regressions. One possible reason is that the standard investment data only focus on investment in capital stock. When existing capital is utilized more intensively, more investment is also needed to maintain it. Such a maintenance investment can be large; it is estimated to be 30% of the investment in new physical capital, according to survey data from Canada (see McGrattan and Schmitz, 1999). While comprehensive maintenance investment data are not directly available, industrial electricity usage is a good proxy, as higher electricity use reflects more intensive capital utilization and implies more maintenance investment. From a real-life investment point of view, the industrial electricity usage growth rate is, in our view, a superior return predictor, as it can be easily calculated almost in real time. In contrast, the benchmark in-sample output measure described by Cooper and Priestley (2009) requires estimation using a full sample. When we compare the industrial electricity usage growth rate to the out-of-sample output gap, both lagged by two months so investors can use them in real time, it is clear that the former outperforms the latter completely, across all forecasting horizons. Our paper contributes to the long line of literature on stock return predictability. such as Campbell (2003), Cochrane (2008), Lamont (2000), Lettau and Ludvigson (2001), Lustig and van Nieuwerburgh (2005), Lettau and Ludvigson (2010), Santos and Veronesi 8

9 (2006), Rangvid (2006), Cooper and Priestley (2009), Belo and Yu (2013), and Rapach and Zhou (2013) among many others. Fama and French (1989) suggest that financial variables correlate with business cycle and can predict stock returns. Also, behavioral variables such as investor sentiment (Baker and Wurgler (2006), Charoenrook (2003)) and consumer confidence (Fisher and Statman (2003), Ludvigson (2004)), can also predict stock returns. Several papers, such as Campbell (2003), Cochrane (2008), and Lettau and Ludvigson (2009), show that price-based financial variables tend to predict stock returns better than quantity-based macroeconomic indicators. In fact, typical business cycle indicators such as GDP do not forecast stock returns (Pena, Restoy, and Rodriguez, 2002). We find that industrial electricity usage growth, by overweighting the most businesscycle-sensitive industries, predict stock returns well. Our paper thus contributes to the literature by linking financial markets and the real economy. The rest of the paper proceeds as follows. Section 2 describes the data and provides summary statistics for the main variables. Sections 3 and 4 present our empirical results from monthly and annual regressions, respectively. Section 5 examines the predictive power in real time. Section 6 concludes. 2 Data 2.1 Electricity and Weather Data Monthly industrial electricity usage data (millions of kilowatt-hours) in the United States are manually collected from two sources: the Energy Information Administration s (EIA) Electric Power Statistics for data from and Electric Power Monthlies for data from As electricity consumption data can be revised by the EIA, our hand 4 EIA Form 826 describes the customers. The residential sector consists of living quarters for private households. The commercial sector consists of service-providing facilities, such as businesses, governments, and institutional living quarters. The industrial sector consists of facilities for producing goods, 9

10 collection of vintage data minimizes any potential forward-looking bias, which is an important concern when conducting return predictability tests. The vintage data are usually available within two months at most. In other words, January s electricity usage is available by the end of March. A key concern with monthly electricity usage data is the strong within-year seasonal effects, caused by such things as weather fluctuations. For example, Figure 1 shows normalized electricity usage (Panel A) and energy degree days (EDD) for each month (Panel B). EDDs are the sum of cooling degree days (CDD) and heating degree days (HDD), which measure summer and winter weather variation, respectively. 5 As shown in the figure, industrial electricity usage, the focus of our paper, is stable within the year, and weather fluctuation is less likely to affect industrial electricity consumption. To further alleviate the seasonality effect, we compute year-over-year growth rates in industrial electricity usage between the same months in two successive years, and thus identify differences in demand due to changes in economic conditions rather than seasonal weather effects. One may argue that year-over-year electricity usage growth is still subject to residual weather effects (for instance, if December 2014 is unusually cold compared to other Decembers). To that end, we also orthogonalize year-over-year electricity growth rates on weather changes measured with EDD. We find that residual electricity usage growth performs similarly, if not slightly better, in predicting stock returns. such as manufacturing (NAICS codes 31-33); agriculture, forestry, and hunting (NAICS code 11); mining, including oil and gas extraction (NAICS code 21); natural gas distribution (NAICS code 2212); and construction (NAICS code 23). Other customers include public street and highway lighting, public authorities, railroads and railways, and irrigation, as well as interdepartmental sales. Total electricity usage accounts for the amount used by ultimate customers, and hence excludes resold or wasted amounts. It also excludes direct use, which is electricity used in power plants for generating electricity. 5 Summer (winter) weather is measured by monthly cooling (heating) degree days (CDD or HDD), which we obtain from the National Oceanic and Atmospheric Administration (NOAA). The daily CDD (HDD) values capture deviations in daily mean temperatures above (below) 65 o F, the benchmark at which energy demand is low. As an example, if the average temperature is 75 o F, the corresponding CDD value for the day is 10 and the HDD is 0. If the average temperature is 55 o F, the corresponding CDD value for the day is 0 and the HDD is 10. Monthly CDD (HDD) values are the sum of the daily CDD (HDD) values in each month. CDD and HDD values are computed from mean temperatures for the United Kingdom and Japan. Mean temperatures are obtained from the Met Office Hadley Centre for the United Kingdom, and the Japan Meteorological Agency for Japan. 10

11 Annual industrial electricity consumption data for Japan and the United Kingdom are obtained from the International Energy Agency s Energy Balances of OECD countries. 2.2 Output Measures We consider several output growth measures. Monthly industry production data are obtained from the Federal Reserve Bank of St. Louis s Economic Data (FRED) website. With the monthly date, we can compute year-over-year output growth as the year-overyear growth rate in monthly industrial production, similar to the industrial electricity usage growth rate. Quarterly industrial production data are obtained from the Board of Governors of the Federal Reserve System (for the United States), the Office for National Statistics (for the United Kingdom), and the Ministry of Economy (for Japan). We compute two alternative annual output growth rates from these quarterly data. Output growth Q4-Q4 refers to the log difference of the industrial production index in the fourth quarter of a given year and in the fourth quarter of the previous year. The year-over-year growth rate alleviates seasonality in the output data. Output growth Q3-Q4 refers to the log difference of the industrial production index in the fourth quarter of this year and in the third quarter of a given year. Moller and Rangvid (2014) show that output growth rates from the third to the fourth quarter of this year predict the stock market returns of next year well. The industrial production index is subject to later revisions, and we use the final revised numbers instead of the vintage data as originally announced. This means that output growth rates are computed using more updated information than the electricity growth rates. We collect industrial production data for 14 industries from the St. Louis Fed from January of 1972 to December of The purpose is to investigate how sectoral industrial productions growth rates relate to the growth rate of aggregate industrial electricity usage, and provide explanations for the industrial electricity usage growth rate s ability 11

12 to forecast future stock returns. We follow Kenneth French s industrial classification and focus on the 17 industries. Since industrial production for banking, retail, and other industries is not available, we are left with 14 industries. They are: steel, machinery, durable, fabricated products, construction, clothes, consumer products, chemicals, utilities, cars, oil, mines, transportation, and food. We compute the sectoral growth rates of industrial production as changes in the log index level of industrial production each month, relative to the level a year ago. We compute the output gap measure following Cooper and Priestley (2009). 6 In the United States, we regress the log of monthly industrial production on a time trend and the square of the time trend. The residual is the estimated output gap. To avoid using forward-looking data, we also follow Cooper and Priestley to compute an out-ofsample output gap using expanding-rolling-window regressions. In particular, at the end of month t in year j, we estimate the output gap regression using data from January 1927 up to that month and compute the out-of-sample output gap using the residual in that month. For the next month, we re-estimate the output gap regression using all data from January 1927 up to month t + 1 to compute the out-of-sample output gap in month t + 1. In the United Kingdom and Japan, to match the frequency of the available electricity data, we use annual industry production data to compute the annual output gap. The sample period for the output gap calculation covers for the United States, for the United Kingdom, and for Japan. Another related measure is the capacity utilization index reported in the Federal Reserve Board s G.17 release. This index is constructed using potential output from a survey of plants and actual output, and measures the proportion of firm capacity that is being used. We compute the growth of capacity utilization as the change in the log 6 We verify that the output gap we computed closely replicates the one used in Cooper and Priestley (2009) using a short overlapping sample up to 2005, when their data ends. 12

13 index level of capacity utilization in each month, relative to its level a year ago. This data is seasonally adjusted and available from 1968 to Investment growth Q3-Q4 (Q4-Q4) is the growth rate of the fourth quarter per capita investment relative to those of the current year s third quarter or the previous year s fourth quarter. Investment data are obtained from the Fed. 2.3 Other Data Excess returns are value-weighted returns in excess of the T-bill rate, and are obtained from the website of Kenneth French. We also consider the forecasting variables investigated by Welch and Goyal (2008), Campbell and Thompson (2008), and Ferreira and Santa-Clara (2011). The details of these variables are as follows. The dividend-price ratio is the difference between the log of dividends and the log of prices. The earnings-price ratio is the difference between the log of earnings and the log of prices. The book-to-market ratio is the ratio of book value to market value for the Dow Jones Industrial Average. The Treasury bill rate is the secondary market rate on three-month T-bills. The default spread is the difference of yields on BAA- and AAA-rated corporate bonds. The term spread is the difference of yields on long-term government bonds and three-month T-bills. The net stock issue is the ratio of 12-month moving sums of net issues by NYSE-listed stocks divided by the total end-of-year market capitalization of NYSE stocks. Inflation is the change in the log of the Consumer Price Index. The long-term rate of return on government bonds is taken from Ibbotson s SBBI Yearbook. Stock return variance is computed as the sum of squared daily returns of the S&P 500. We take these data from Amit Goyal s website; more details of data construction are provided by Welch and Goyal (2008). The NBER expansion is the fraction of months spent in expansion in each year; monthly NBER expansion data are obtained from the NBER website. 13

14 2.4 Summary Statistics Panel A of Table 1 presents summary statistics for our main variables of interest at annual frequency. The sample covers in the United States (55 years), in the United Kingdom (39 years), and in Japan (29 years). The December-to-December annual industrial electricity growth rate in the United States has a mean of 1.09% and a standard deviation of 5.69%. The annual industrial electricity growth rates have lower means and are less volatile in the United Kingdom and Japan, possibly due to a shorter and more recent sample period. The weather-adjusted electricity growth rate in the United States, as a regression residual, has a mean of zero by construction. 7 Its standard deviation of 5.28% is only slightly smaller, suggesting that the bulk of the variation in the raw industrial electricity growth rate is unrelated to weather change. Similar patterns are observed in the United Kingdom and Japan as well: orthogonalizing industrial electricity growth on weather fluctuation hardly changes its volatility. The autocorrelations for industrial electricity growth rates are relatively low: in the United States, in United Kingdom, and in Japan. The average annual (Q4-Q4) industry production growth is highest in the United States (2.66%), followed by Japan (2.04%), and is the lowest in the United Kingdom (0.89%). The growth rate is most volatile in Japan (5.23%), followed by the United States (4.53%), and then the United Kingdom (3.76%). In the United States, not surprisingly, the December-to-December output growth rate has about the same mean as the Q4-Q4 output growth rate, but is more volatile. Panel A also shows that the in-sample output gap does not have a mean of zero in all three countries, because it is estimated in a regression using all available data over a longer sample period in each country. Since the output gap measures deviation from long- 7 Specifically, we regress December-to-December industrial electricity growth on the December-to- December change in EDD and use the residuals from the regression. 14

15 term trends, it is more autocorrelated than the annual growth rates of both industrial electricity usage and production. For example, the annual autocorrelation of the output gap is in the United States, in the United Kingdom, and in Japan. In the United States, where quarterly investment data is available, we find investment growth rates (Q3-Q4 and Q4-Q4) to have similar means to the corresponding output growth rates, but they tend to be much more volatile. December-to-December capital utilization in the United States has a mean of , with a standard deviation of More months are in expansion periods than contraction periods as shown by the mean, which is There is substantial variation in EDD growth: while the mean is only , the standard deviation is We find similar patterns of EDD growth in the United Kingdom and Japan, where the mean is small but the standard deviation is large. Panel B reports correlations among the key variables. Several interesting patterns emerge. First, industrial electricity usage growth rates closely track the growth rates in industry production in all three countries. In the United States, the correlations between industrial electricity usage growth rates and output growth rates are above 60%. Similarly, higher correlations are observed in the United Kingdom and Japan. Figure 2 provides a visualization of these high correlations, which supports our view that industrial electricity usage is tracking capital services in real time. Given the high correlations with output measures, it is not surprising that the industrial electricity growth rate is a good business cycle indicator. For example, in the United States, the correlation between the industrial electricity growth rate and the NBER expansion indicator is 61%. The important difference is that the industrial electricity usage growth rate is observed almost in real time, while NBER expansion/recession dates are often released with significant delays. The correlations between the industrial electricity growth rate and investment growth rates are also high (above 50%). 15

16 Second, as highlighted in Figure 1, industrial electricity usage is partially driven by weather change. The correlation between December-to-December industrial electricity usage growth and annual EDD growth is 29.21% in the United States. Orthogonalizing December-to-December industrial electricity usage growth on December-to-December EDD growth greatly alleviates the weather effect. The residual has a much lower correlation, 6.39%, with annual EDD growth, yet remains highly correlated with other output measures and the business cycle indicator. Moreover, it is highly correlated (92.66%) with the raw electricity growth rate. We find similar patterns in Japan and the United Kingdom. In both countries, the growth rates of raw annual industrial electricity usage are positively correlated with changes in annual EDD (the correlations are 16.59% (Japan) and 19.56% (United Kingdom)). The residuals from regressing annual industrial electricity usage growth on annual EDD growth in these two countries, by construction, are uncorrelated with annual EDD growth. Finally, in all three countries, we observe evidence that supports a countercyclical risk premium. Industry output measures in year t are negatively correlated with stock market excess returns in year t + 1, consistent with the notion that the risk premium increases during a recession. For the remainder of the paper, we will formally analyze the predictive power of the industrial electricity usage growth rate, especially relative to various measures of industry output growth. 3 Monthly Predictive Regressions Since monthly industrial electricity consumption data is available in the United States, we first conduct predictive regressions at monthly frequency in order to maximize the power of the test. To alleviate the impact of seasonality, we use a year-over-year growth rate in industrial electricity usage. For example, we use the electricity growth rate from 16

17 January of year t 1 to January of year t to predict excess stock returns in February of year t. Then we use the electricity growth rate from February of year t 1 to February of year t to predict excess stock returns in March of year t, and so on. As a result, the monthly predictive regressions will be overlapping. 3.1 The In-Sample Predictability of Electricity Growth In this subsection, we conduct the standard overlapping in-sample forecasting exercise. For each month from 1956 to 2010, we use a year-over-year industrial electricity usage growth rate (January-to-January, February-to-February, etc.) to predict excess, as well as actual, stock market returns in the next month, three months, six months, nine months, and twelve months. Due to the overlapping nature of such a regression, we present the Hodrick (1992) t-value (Hodrick-t). Besides persistent regressors, the evaluation of predictive regressions needs to properly account for the effect of a short sample and estimation with overlapping data. To consider persistent predictors, overlapping regressions, and a short sample simultaneously, we compute the p-values of coefficients through simulation, following Li, Ng, and Swaminathan (2013). We illustrate our simulation procedure using a bivariate regression where the predictive variables are industrial electricity growth (EG) and the output gap (Gap). We denote the excess return r e. Define a 3 1 column vector Z t = [rt e, EG t, Gap t ]. We first estimate a first-order vector autoregression (VAR): Z t+1 = A 0 + A 1 Z t + u t+1. We impose the null hypothesis of no return predictability by setting the slope coefficients of the r e t equation to zero and the intercept of the equation to the empirical mean of rt e. The fitted VAR is then used to generate T observations of the simulated variables [rt e, EG t, Gap t ]. The initial observations are drawn from a multivariate normal distribution of the three variables, with the mean and the covariance matrix set to their empirical counterparts. Once the 17

18 initial observations are chosen, the subsequent T 1 simulated observations are generated from the fitted VAR with the shocks bootstrapped from the actual VAR residuals (sampling without replacement). These simulated data are then used to run a bivariate return predictive regression to produce regression coefficients. We repeat the process 50,000 times to obtain the empirical distribution of the regression coefficients (under the null of no predictability) and the R-squared, which in turn produces the p-values associated with our actual estimated coefficients and the p-value associated with the R-squared. The results are reported in Table 2. Panel A indicates that that simple year-over-year industrial electricity usage growth rate has strong predictive power for future excess stock market returns. In particular, an increase in industrial electricity usage today predicts lower future excess stock returns, consistent with a countercyclical risk premium. The regression slope coefficients for electricity growth are statistically highly significant. Their magnitudes increase with the forecast horizon. At the annual horizon, a 1% increase in the year-over-year electricity growth rate predicts an excess stock return that is 0.92% lower, with an R-squared of 8.64%. The p-values at all horizons strongly reject the null that these predicting coefficients are zeros. In addition, the p-values for the R-squared are also highly significant, suggesting that it is very unlikely to observe our R-squared when the industrial electricity usage growth rate has no return predictive power. We also report the implied R-squared (R 2-0) that a variable obtains under the null of no predictability in returns, following Boudoukh, Richardson, and Whitelaw (2005) and Cooper and Priestley (2009). Specifically, the adjusted R-squared is computed as: R 2-0 = ( ) 2 1+ ρ(1 ρk 1 ) 1 ρ R 2, (1) k where ρ is the autocorrelation coefficient of the predictor variable, k is the horizon, and 18

19 R 2 is the empirical R-squared. The implied R-squared provides us with an economic sense of how far the R-squared of a predicting variable deviates from the R-squared this variable generates, given its persistence and no predictability. For instance, given the persistence of electricity growth, even if there is no predictability in returns, the R-squared will be 4.27%. But electricity growth s actual R-squared is 8.64%, which is twice the R-squared generated under the null of no predictability. 8 It is evident that the actual R-squares achieved by electricity growth at various forecasting horizons are substantial improvements over those produced under the null of no predictability. Using the simulated distribution of the adjusted R-square, we confirm that these improvements are statistically significant, with the associated p- values overwhelmingly under 1% at all horizons. The year-over-year electricity growth rate is still subject to weather effects, as is evident in Panel B of Table 1. To that end, we try to orthogonalize these year-over-year electricity growth rates on weather fluctuation, measured by the year-over-year growth rate in monthly EDD, so that we can focus on residual electricity usage growth. Panel B reports the predictive regression results using weather-adjusted electricity growth rates. The results are very similar. Overall, it is clear that seasonality and weather effects are not driving the return predictive power of industrial electricity data. We confirm that weather-adjusted electricity growth rates provide results similar to those of the raw growth rates in all other tests, and in Japan and the United Kingdom as well. For brevity, in the rest of the paper, we only present results using the raw growth rates, which are easy to compute and do not suffer from forward-looking bias. Panels C and D repeat the analysis from Panels A and B with risk free rates, and we find strong predictive power as well. In particular, a higher industrial electricity growth today predicts higher risk free rates up to a year, suggesting that industrial electricity 8 For predicting next-monthly excess returns (k=1), the two R-squares are identical since the regression does not use an overlapping sample. 19

20 usage growth is highly pro-cyclical. 3.2 The In-Sample Predictability of Other Predictors To put the predictive power of industrial electricity growth into perspective, we examine fourteen other monthly return predictors, one at a time, in the same monthly overlapping predictive regressions. The first ten predictors are well-known financial variables: dividend-price ratio, earnings-price ratio, book-to-market ratio, the Treasury bill rate, the default spread, the term spread, net equity issuance, inflation, the return on long-term government bonds, and stock variance. We also consider four other measures of output growth: the in-sample output gap calculated using the full sample, the out-of-sample output gap computed using the expanding rolling sample, the year-over-year change in capacity utilization, and the year-over-year growth rate of industrial production. Table 3 presents the performance of these alternative predictors by themselves. Among the financial variables, judging by the p-values associated with the regression coefficients, inflation and long-term bond returns have significant predictive power, but their R- squares are noticeably lower than those of the industrial electricity growth rate at all horizons. The performance of the financial ratios appears weak in our sample for two reasons. First, our sample starts in 1956 rather than in Second, our statistical inference corrects for the biases caused by having a persistent predictor in overlapping regressions. Financial ratios, which tend to be more persistent, naturally become weaker after this correction. The four industrial-output-based measures predict excess stock market returns better than the financial variables. The strongest predictor among the four is the in-sample output gap. It significantly predicts stock returns at all horizons and the accompanying adjusted R-squares are even higher than those of the industrial electricity usage growth rate. However, the in-sample output gap is computed using future information, which 20

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